The non-destructive investigation of samples is an important objective in various technical fields like material sciences, non-destructive testing, medical examinations, archaeology, construction technique, techniques concerning security matters etc. One approach for obtaining an image of a sample e.g. by computer tomography (CT) is based on an irradiation through a sample plane from different projection directions with X-rays, followed by the reconstruction of the sample plane on the basis of attenuation data measured at different directions. The entirety of the measured attenuation data can be described in terms of so-called Radon data in a Radon space.
Different reconstruction methods for Radon data are known today (see e.g. the textbooks “Computed Tomography-Fundamentals, System Technology, Image Quality, Applications” by W. A. Kalender (1st edition, ISBN 3-89578-081-2); “Image Reconstruction from Projections: The Fundamentals of Computerized Tomography” by G. T. Herman, Academic Press, 1980; and “Einführung in die Computertomographie” by Thorsten M. Buzug (Springer-Verlag, Berlin 2004)). The conventional reconstruction methods can be summarized as iterative reconstruction methods and filtered back-projection methods.
The iterative reconstruction is an approximation method based on a plurality of iteration steps. The essential disadvantage of the iterative reconstruction of higher resolution images is that the iteration leads to extremely long calculation times. The filtered back-projection method relies in principle on the Fourier-slice theorem describing a relationship between the Fourier transform of the Radon data and Fourier transformed image data. A general disadvantage of using the Fourier-slice theorem lies in the fact that an interpolation step in the reconstruction results in errors and artifacts which have a tendency to increase with increasing space frequency. This disadvantage can only be avoided by using detectors with high resolution. However, the application of these detectors is limited in terms of dose burden, costs and data processing time.
An improved method of reconstructing image functions from Radon data is described in EP 04031043.5 (unpublished on the filing date of the present patent specification). With this method of using orthogonal polynomial expansions on the disk (in the following: OPED algorithm), an image function representing the region of investigation is determined from Radon data as a sum of polynomials multiplied with values of projection profiles measured corresponding to a plurality of predetermined projection directions through the region of investigation. The projection profile for each projection direction is constructed with projection values (attenuation values) detected with selected groups of e.g. X-ray irradiation beam components being parallel to said projection direction. The irradiation is emitted by an X-ray source at different views (or: angular positions) relative to the region of investigation. With the OPED algorithm as described in EP 04031043.5, the number of protection directions as well as the number of projection values in each projection profile typically is equal to the number of views.
The OPED algorithm has essential advantages in particular in terms of computational time reduction and producing images with improved signal-to-noise ratio. Furthermore, the imaging resolution can be improved in particular by using an increased number of detector elements with correspondingly reduced size. However, the improvement of the imaging resolution can be limited by the number of views. As the number of views is restricted with a typical computer tomography device to about 1.000 per full circle, an increased number of detector elements exceeding this value does not automatically yield an increased number of complete projection profiles. If the number of views is smaller than the number of detector elements, predetermined projection lines parallel to a particular projection direction are not irradiated through the region of investigation so that corresponding parallel beam components are not provided and related projection values cannot be measured. As the result, the projection profiles are incomplete and the image cannot be reconstructed correctly. A corresponding disadvantage can occur with the above mentioned filtered back-projection method.
A particular disadvantage of the OPED algorithm can occur as an adjustment of the reconstructed area to the area of the object without changing the scanning geometry is not easily possible with the OPED algorithm. In particular, the OPED algorithm as described in EP 04031043.5 has a drawback if zooming into the object is necessary. An example is given by the imaging of a part of a human body, e.g. a leg in a CT device. Only a few beam components of a fan beam covering the whole gantry will hit the leg, so that the projection profiles will contain only a few measured values for image reconstruction. Many data outside the leg would be set to be zero and the full potential of the OPED algorithm would not be used. An unsharpness of the leg image could be avoided by changing the fan beam and detector geometry only.
Another algorithm for the reconstruction of two-dimensional images from projections is described by T. Bortfeld et al. in “Phys. Med. Biol.”, vol. 44, 1999, p. 1105-1120. The images are reconstructed from measured projection profiles, which are provided by projection values corresponding to parallel equidistant projection lines. As angle positions of the fan beam components are not identical with angle positions of an irradiating source in practice, the projection profiles are obtained by a rebinning step including an interpolation. This means that in a sinogram to be used for reconstruction the most positions are empty and interpolation is used for all these positions between neighboured not directly used measured values. However, the above potential problems of the OPED algorithm cannot be solved with the reconstruction technique of T. Bortfeld et al.
The above disadvantages are associated not only with the conventional CT image reconstruction, but also with all other image reconstructions based on Radon data.